Checking date: 10/04/2024

Course: 2024/2025

Mathematics for Data Science
(17752)
Master in Statistics for Data Science (Plan: 386 - Estudio: 345)
EPI

Coordinating teacher: BRANDLE CERQUEIRA, CRISTINA

Department assigned to the subject: Mathematics Department

Type: Compulsory
ECTS Credits: 3.0 ECTS

Course:
Semester:

Requirements (Subjects that are assumed to be known)
None
Objectives
Use advanced knowledge of Linear Algebra for its application in methods of analysis of large volumes of data. Understand the foundations of the algorithms used in the analysis of large volumes of data in order to interpret the results and their meaning and validity. Specifically: 1) Study of matrix algebra 2) Proficiency of least squares techniques 3) Proficiency of singular value decomposition techniques
Skills and learning outcomes
Description of contents: programme
1. Matrices (a) Matrix Operations (b) Change of Basis Matrix (c) Matrix of a Linear Transformation 2. Linear Systems of Equations (a) LU factorization (b) Cholesky factorization (c) Applications: Iterative Methods 3. Diagonalization (a) Diagonalization (b) Orthogonal Diagonalization (c) The Power Method (d) Markov processes 4. Least Squares Problems (a) Data fitting (b) Orthogonal projections and Least square problems (c) QR factorization (d) Constrained LSP 5. Singular Value Decomposition (a) Singular Value Decomposition (b) The pseudoinverse (c) Principal component analysis
Learning activities and methodology
The classes consist of a mixture of presentations referring to the subject and practical use through the resolution of exercises. * Training activities   - AF1: Theoretical lesson.   - AF2: Practical lesson.   - AF5: Tutorials.   - AF7: Individual work.   - AF8: On-site evaluation tests. * Teaching methodologies   - MD1: Class lectures by the professor with the support of computer and audiovisual media, in which the main concepts of the subject are developed and the bibliography is provided to complement the students' learning.   - MD2: Critical reading of texts recommended by the professor of the subject: press articles, reports, manuals and/or academic articles, either for later discussion in class, or to expand and consolidate the knowledge of the subject.   - MD3: Resolution of practical cases, problems, etc. posed by the teacher individually or in groups.   - MD4: Presentation and discussion in class, under the moderation of the professor of topics related to the content of the subject, as well as case studies.   - MD5: Preparation of papers and reports individually or in groups.
Assessment System
• % end-of-term-examination 60
• % of continuous assessment (assigments, laboratory, practicals...) 40

Calendar of Continuous assessment

Basic Bibliography
• David C. Lay, Steven R. Lay, Judi J. McDonald. Linear Algebra and Its Applications. Pearson; 5 edition. 2016
• Lloy N. Trefethen; David Bau, III. Numerical Linear Algebra Twenty-Fifth Anniversary Edition. SIAM . 2022
• Timothy Sauer. Numerical Analysis 2e. Pearson . 2012
• W. Keith Nicholson. Linear Algebra with Applications. Lyryx, Open Edition Version. 2021